A new approach based on vector field clustering for tool path optimization of 5-axis CNC machining is presented in this paper. The strategy of the approach is to produce an efficient tool path with respect to the optimal cutting direction vector field. The optimal cutting direction maximizes the machining strip width. We use the normalized cut clustering technique to partition the vector field into clusters. The spiral and the zigzag patterns are then applied to generate tool path on the clusters. The iso-scallop method is used for calculating the tool path. Finally, our numerical examples and real cutting experiment show that the tool path generated by the proposed method is more efficient than the tool path generated by the traditional iso-parametric method.

The traditional method of manipulation of knots and degrees gives poor quality of surface, if compatibility of input curves is not good enough. In this work, a new algorithm of multiple refitting of curves has been developed using minimum energy based formulation to get compatible curves for skinning. The present technique first reduces the number of control points and gives smoother surface for given accuracy and the surface obtained is then skinned by compatible curves. This technique is very useful to reduce data size when a large number of data have to be handled. Energy based technique is suitable for approximating the missing data. The volumetric information can also be obtained from the surface data for analysis.

As three-dimensional range scanners make large point clouds a more common initial representation of real world objects, a need arises for algorithms that can efficiently process point sets. In this paper, we present a method for extracting smooth surfaces from dense point clouds. Given an unorganized set of points in space as input, our algorithm first uses principal component analysis to estimate the surface variation at each point. After defining conditions for determining the geometric compatibility of a point and a surface, we examine the points in order of increasing surface variation to find points whose neighborhoods can be closely approximated by a single surface. These neighborhoods become seed regions for region growing. The region growing step clusters points that are geometrically compatible with the approximating surface and refines the surface as the region grows to obtain the best approximation of the largest number of points. When no more points can be added to a region, the algorithm stores the extracted surface. Our algorithm works quickly with little user interaction and requires a fraction of the memory needed for a standard mesh data structure. To demonstrate its usefulness, we show results on large point clouds acquired from real-world objects.

A non-uniform 3-point ternary interpolatory subdivision scheme with variable subdivision weights is introduced. Its support is computed. The $C^0$ and $C^1$ convergence analysis are presented. To elevate its controllability, a modified edition is proposed. For every initial control point on the initial control polygon a shape weight is introduced. These weights can be used to control the shape of the corresponding subdivision curve easily and purposefully. The role of the initial shape weight is analyzed theoretically. The application of the presented schemes in designing smooth interpolatory curves and surfaces is discussed. In contrast to most conventional interpolatory subdivision scheme, the presented subdivision schemes have better locality. They can be used to generate $C^0$ or $C^1$ interpolatory subdivision curves or surfaces and control their shapes wholly or locally.

Different CAx systems are being utilized throughout the product lifecycle due to the practical reasons in the supply chain and design processes. One of the major problems facing enterprises of today is how to share and exchange data among heterogeneous applications. Since different software applications use different terminologies, it is difficult to share and exchange the product data with internal and external partners. This paper presents a method to enhance the CAD model interoperability based on feature ontology. The feature ontology has been constructed based on the feature definition of modeling commands of CAD systems. A method for integration of semantic data has been proposed, implemented, and tested with two commercial CAD systems.

Interpreting a natural line drawing as a solid object requires simplifying assumptions in order to make the problem more tractable. Unfortunately, some of the assumptions made in the past have overly simplified the problem. Restricting the valency of vertices, and in particular allowing only trihedral vertices, distorts the problem, since algorithms which are satisfactory for the simplified problem are not satisfactory in the general case. This paper presents a test set of drawings of objects with higher-valency vertices. The intention in creating this test set is that it may be used to determine how effective various algorithms are in dealing with general (i.e. unrestricted) valency vertices.

Euclidean Voronoi diagram of spheres in 3-dimensional space has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this, paper is the topological representation for Euclidean Voronoi diagram of spheres which is a typical non-manifold model. The proposed representation is a variation of radial edge data structure capable of dealing with the topological characteristics of Euclidean Voronoi diagram of spheres distinguished from those of a general non-manifold model and Euclidean Voronoi diagram of points. Various topological queries for the spatial reasoning on the representation are also presented as a sequence of adjacency relationships among topological entities. The time and storage complexities of the proposed representation are analyzed.

As collaborative design and configuration design gain increasing importance in product development, it becomes essential to exchange parametric CAD models among participants. Parametric CAD models can be represented and exchanged in the form of a macro file or a part file that contains the modeling history of a product. The modeling history of a parametric CAD model contains feature specifications and each feature has selection information that records the name of the referenced topological entities. Translating this selection information requires solving the problems of how to identify the referenced topological entities of a feature (persistent naming problem) and how to convert the selection information into the format of the receiving CAD system (naming mapping problem). The present paper introduces the problem of exchanging parametric CAD models and proposes a solution to naming mapping.

This is a report on a new methodology to manage design knowledge by utilizing a knowledge-based CAD and a prototype system named $C^3$ (Cubic; CAD knowledge Code Capacitor), which is being developed using our methodology. $C^3$ facilitates (i) the automatic generation of a knowledge code for a knowledge-based CAD by processing design documents written in the format near the natural language, such as English or Japanese, and (ii) automatically generation of a design document written in the format near the natural language from the knowledge code. The features of the system facilitate document-based design knowledge management which reduces the designer's load to encode and maintain design knowledge, because it is easier for a designer to treat a natural language description than a coded description.

This paper presents a scheme for interpolating intersecting uniform cubic B-spline curves by Catmull-Clark subdivision surfaces. The curves are represented by polygonal complexes and the neighborhoods of intersection points are modeled by X-Configurations. When these structures are embedded within a control polyhedron, the corresponding curves will automatically be interpolated by the surface limit of subdivision of the polyhedron. The paper supplies a construction which clearly shows that interpolation can still be guaranteed even in the absence of symmetry at the X-configurations. In this sense, this scheme generalizes an already existing technique by the same authors, thereby allowing more freedom to designers.

This paper introduces an approach to an ontology-based multi-level knowledge framework for a knowledge management system for discrete-product development. Participants in a product life cycle want to share comprehensive product knowledge without any ambiguity and heterogeneity. However, previous knowledge management approaches are limited in providing those aspects: therefore, we suggest an ontology-based multi-level knowledge framework (OBMKF). The bottom level, the axiom, specifies the semantics of concepts and relations of knowledge so ambiguity can be alleviated. The middle level is a product development knowledge map; it defines the concepts and the relations of the product domain knowledge and guides the engineer to process their engineering decisions. The middle level is then classified further into more detailed levels, such as generic product level, specific product level, product version level, and manufactured item level, according to the various viewpoints. The top level is specialized knowledge for a specific domain that gives the solution of a specific task or problem. It is classified into three knowledge types: expert knowledge, engineering function knowledge, and data-analysis-based knowledge. This proposed framework is based on ontology to accommodate a comprehensive range of knowledge and is represented with first-order logic to maintain a uniform representation.